An earthquake would be impossible to capture in still images given that they can occur so suddenly and violently. They only last a few seconds so by the time you come to your senses and get your camera out it will most likely have ended. The aftermath is what you will want to quickly capture not the actual quake. I guess there is always the chance that you are taking pictures of something when the quake starts and you might capture damage as it happens but I doubt you'll get a clear "perfect" photo with the ground shaking.

Documenting a natural disaster as it happens is something you obviously want to capture with video instead. However your first priority should always be your own safety. There is a reason you don't see beautiful HDR landscapes of a beach while a Hurricane/Typhoon is coming ashore!

I'll wait for the resurrected Nikonos for that kind of work. I used to take mine to the coast during Pacific storms. Probably not smart, but it was fun. Aquatech makes a housing that's submersible, but not for deep diving. It's rated to only 10m or 33 feet, but it's smaller and lighter than any other.

Here in No. California your first thought is self preservation, not images when an earthquake hits. After that it's the safety of friends, family and neighbors.

An earthquake is simple ... you just shake the camera, someone could throw some rubble off a roof to make it more realistic.
A tsunami is a bit trickier, capturing the real thing could prove fatal. Though you could use a housing and something that makes the camera buoyant so that at least the camera is recovered and used as a last testament to the unlucky photographer.

All joking aside, I don't think I would even try photographing such a disaster. A major storm would be a different matter (perhaps). I couldn't even bring myself to go and capture a burning building or a car crash as I wouldn't really relish the idea of people taking shots (apart from the police/fire dept) if something like this happened to me.